The geometric properties of vector sequence spaces with variable basic sequence of subspaces, including H-property, convexity, Radon-Nikodym property and differentiability of convex functions, are characterized in this parper.

Under the condition that fi(x)≤0(i=1,2,…,p),ρ(x)>0 and f(x),g(x),ρ(x) are differential convex functions,the Kuhn-Tucher optimal condition of the multi-objective vector fractional programming problem is discussed.

Two mathematical derivations of them have been introduced by using the properties of differentiable function and the derivation algorithm of multiple function in present paper, and several mistakes in some derivative methods have also been pointed out.

In this paper, we give a generic condition of differentiable functions on noncompact complete Rie- mannian manifold.

This paper investigates the absolute convergence of the Fourier Laplace series concerning of some smooth functions defined on the unit sphere in R n,hereinto shows that:if f is 2([n4]+1) th continuously differentiable function on H r P(Ω n),then the series ∑∞k=0Y kf(x) converges uniformly to f.

In this paper,by using the result about the simultaneous polynomial approximation with Hermite interpolatory side conditions,we discuss general conformal simultaneous approximation of differentiable functions and obtain some results.